Where \(N\left(t\right)\)  and \(P\left(t\right)\)  are used to represent the size of the prey population at time \(t\)  respectively, \(r\)  and \(s\)  are the intrinsic growth rate for the prey and predator respectively, \(h\)  is a measure of the quality of the prey as food for the predator, \(K\)  is the prey environmental carrying capacity, \(q\)  is the maximum predation rate per capita and \(a\)  is half of the saturated response level [1]}. The growth of the predator and prey population is a logistic form and and the predator environmental carrying capacity is a prey dependant. Note that in this manuscript we will use a type II functional response, i.e. \(H\left(N\right) = qN/\left(N+a\right)\)  [2]}.
